The complexity reduction of well-performing Multiple Input Multiple Output (MIMO) detection schemes has drawn considerable interest recently. Even though sophisticated integrated circuits may be available today for the most complex schemes, including Maximum Likelihood (ML, using sphere decoding), the actual throughput and integration costs of these detectors is out of the scope of projected applications of MIMO systems. Low complexity heuristic methods using techniques derived from equalization provide a simple alternative to algorithmic schemes. However, their poor performance makes them unsuited for most practical applications. Typically, the proportion of wrongly decoded symbols (even in the case of zero-forcing ‘ZF’ or means square error ‘MSE’) represent only a fraction of the transmitted data. Thus, gains in accuracy are derived at the expense of significant losses in performance and increased system complexity.
Multi-carrier transmission over a frequency selective channel implies large differences between the Signal to Noise Ratios (SNR) on the transmitted tones. For independently detected tones, the best performance in terms of average bit error rate (BER) is obtained when conditions are equally good on all sub-carriers, as proved by Jensen's inequality. In the case of precoded Orthogonal Frequency Division Multiplexing (OFDM), independent per dimension minimum square error (MSE) and joint-maximum-likelihood (ML) detections are not equivalent, as tones are no longer independent. Jensen's bound, which is reached by MSE detection, can then be outperformed. However, the computational complexity of joint-ML detection makes it unrealistic in practical systems.